Subgroups — C₁₇×PSL(2,𝔽₁₃) #32915642

Order 18564.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×D₁₃⋊C₃	—	14	1	no	maximal
2	PSL(2,𝔽₁₃)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇×C₁₃⋊C₃	—	14	1	no	Hall
4	C₁₇×D₁₃	—	14	1	no	—
5	D₇×C₁₇	—	78	1	no	maximal
6	C₁₃×C₁₇	—	14	1	no	Hall
7	C₂×D₃×C₁₇	—	91	1	no	maximal, Hall
8	A₄×C₁₇	—	91	1	no	maximal, Hall
9	C₇×C₁₇	—	78	1	no	Hall
10	C₂×C₃×C₁₇	—	91	1	no	—
11	D₃×C₁₇	—	91	2	no	—
12	D₁₃⋊C₃	—	14	1	no	—
13	C₂²×C₁₇	—	91	1	no	Hall
14	C₃×C₁₇	—	91	1	no	Hall
15	C₁₃⋊C₃	—	14	1	no	Hall
16	C₂×C₁₇	—	91	1	no	—
17	D₁₃	—	14	1	no	—
18	C₁₇	PSL(2,𝔽₁₃)	1	1	yes	maximal normal, characteristic, direct product factor, Sylow
19	D₇	—	78	1	no	—
20	C₁₃	—	14	1	no	Sylow
21	C₂×D₃	—	91	1	no	Hall
22	A₄	—	91	1	no	Hall
23	C₇	—	78	1	no	Sylow
24	C₂×C₃	—	91	1	no	—
25	D₃	—	91	2	no	—
26	C₂²	—	91	1	no	Sylow
27	C₃	—	91	1	no	Sylow
28	C₂	—	91	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. PSL(2,𝔽₁₃)	C₁₇	direct (N × H)
18. C₁₇	PSL(2,𝔽₁₃)	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.